I'm doing quadratic equations x^2 +bx+c =0.I'm supposed to factor each polynomial. I know how to questions like x^2 +8x +12 =0 but this one says, j^2-9jk-10k^2. I'm confused
j^2-9jk-10k^2
what adds to 9, multiplies to 10: 10,1
(j-10k)(j+k)
your teacher is just too easy.
I'm in the ninth grade and not the smartest community
To factor the quadratic equation j^2 - 9jk - 10k^2, you need to look for two binomials that multiply together to give you the original quadratic expression. Specifically, you are looking for two binomials in the form (mj + nk) (mj - nk), where m and n are constants.
Here's how you can go about factoring this quadratic equation step by step:
Step 1: Identify the coefficient of the squared term (j^2), which is 1, and the constant term (-10k^2).
Step 2: Find two numbers, let's say A and B, whose product is equal to the product of the coefficient of the squared term (1) and the constant term (-10k^2). In this case, we have A * B = (1)(-10k^2) = -10k^2.
Step 3: Determine the sum of these two numbers A and B, which is equal to the coefficient of the linear term (-9jk). In this case, we have A + B = -9jk.
Step 4: Now, we need to find two numbers A and B that satisfy the following conditions: Their product equals -10k^2 and their sum equals -9jk.
Step 5: Take the coefficient of the squared term (1) and write it as a product of two numbers A and B, such that A * B = -10k^2 and A + B = -9jk. In this case, let's choose A = -10k and B = k.
Step 6: Rewrite the linear term (-9jk) using the numbers A and B from the previous step: -9jk = (-10k + k) * j.
Step 7: Now we can factor out the quadratic equation j^2 - 9jk - 10k^2:
j^2 - 9jk - 10k^2 = (j - 10k)(j + k).
Therefore, the factored form of j^2 - 9jk - 10k^2 is (j - 10k)(j + k).